To find deterministic solutions to the transient SNβ neutron transport
equation, iterative schemes are typically used to treat the scattering (and
fission) source terms. We explore the one-cell inversion iteration scheme to do
this on the GPU and make comparisons to a source iteration scheme. We examine
convergence behavior, through the analysis of spectral radii, of both one-cell
inversion and source iterations. To further boost the GPU parallel efficiency,
we derive a higher-order discretization method, simple corner balance (in
space) and multiple balance (in time), to add more work to the threads and gain
accuracy. Fourier analysis on this higher-order numerical method shows that it
is unconditionally stable, but it can produce negative flux alterations that
are critically damped through time. We explore a whole-problem (in all angle
and all cell) sparse linear algebra framework, for both iterative schemes, to
quickly produce performant code for GPUs. Despite one-cell inversion requiring
additional iterations to convergence, those iterations can be done faster to
provide a significant speedup over source iteration in quadrature sets at or
below S128β. Going forward we will produce a two-dimensional implementation
of this code to experiment with memory and performance impacts of a
whole-problem framework including methods of synthetic acceleration and
pre-conditioners for this scheme, then we will begin making direct comparisons
to traditionally implemented source iteration in production code.Comment: 11 pages, 4 figures, M\&C 2023 ANS conferenc